Towards noise-resilient quantum optimization

The adiabatic algorithm is a promising algorithm for finding the ground states of Hamiltonians. However, its implementation is generally sensitive to noise that causes excitations from the adiabatic ground state. Correcting these excitations in a fault-tolerant way is impractical for near-term experiments. Nevertheless, by co-designing implementations to address the dominant noise sources in a given experimental platform, one can significantly mitigate the effects of noise. In this work, we develop a framework for characterizing the effects of dissipation and non-adiabaticity on the adiabatic algorithm. We apply it to study intermediate-state spontaneous emission in neutral atom arrays during adiabatic evolution [Ebadi et al. arXiv:2012.12281]. We show that in systems of neutral atoms with Rydberg interactions, such spontaneous scattering is less destructive than the bare emission rates suggest. Next, we compare two classes of algorithms with identical Hamiltonian dynamics, and show that they have very different noise properties. We give simple conditions for choosing the more noise-robust version of the two. Finally, we design and analyze a STIRAP-inspired protocol which minimizes the number of emission events during the algorithm.